The speed-distance-time triangle is one of the most useful formulas in everyday maths. Here are all three versions of the formula, worked examples, and real-world applications.
Whether you're calculating journey times, working out if a car was speeding, or figuring out how long a run will take, the speed-distance-time relationship is the tool you need. It's one formula, three arrangements.
A simple memory aid: draw a triangle with D at the top, S bottom-left and T bottom-right. Cover the one you want to find — the remaining two show whether to multiply or divide.
The most common mistake is mixing units. If speed is in km/h, distance must be in km and time in hours. If you mix miles with hours and kilometres, the answer will be wrong.
Example 1 — Journey time: You're driving 240km at an average speed of 90 km/h. How long will it take?
Example 2 — Average speed: A runner completes a half marathon (21.1km) in 1 hour 58 minutes. What was their average speed?
Example 3 — Distance: A plane flies at 850 km/h for 3 hours 45 minutes. How far does it travel?
Here's a classic trap: if you drive to a destination at 60 km/h and return at 40 km/h, what's your average speed for the whole journey?
Most people say 50 km/h. The correct answer is 48 km/h. The mistake is that you spend more time at the lower speed, so it has more weight in the average.
When two objects move toward each other, their closing speed is the sum of their speeds. When moving in the same direction, the relative speed is the difference.
Athletes often use pace (time per unit distance) rather than speed (distance per unit time). They're the same information expressed differently: